Remote-sensing observations with instruments aboard the High Altitude and Long Range Research Aircraft (HALO) are used for this study. Airborne lidar observations have been performed during the Mid-latitude Cirrus experiment (ML-CIRRUS, March and April 2014; ) and the Cirrus at High Latitudes experiment (CIRRUS-HL, June and July 2021; ). Those experiments focused on investigating the microphysical, optical, and radiative properties of cirrus clouds and contrail cirrus, with flight planning supported by simulations with the contrail cirrus prediction model CoCiP . Naturally, these observations feature a high likelihood of serendipitous observations of embedded contrails. Details of the research flights conducted during ML-CIRRUS and CIRRUS-HL can be found in Table 3 and Table 1, respectively.

The WAter vapor Lidar Experiment in Space (WALES) instrument combines the differential absorption lidar (DIAL) technique for water vapor profiling with the high spectral resolution lidar (HSRL) technique for aerosol profiling. It provides height-resolved aerosol observations in the form of the backscatter coefficient (β) at 532 and 1064 nm, the extinction coefficient (α) at 532 nm, and the particle linear depolarization ratio (PLDR, δ) at 532 nm . Data are collected with an integration time of 0.2 s and a vertical resolution of 15 m. The detection limit is approximately at a backscatter ratio of R = 1.01 at 2 km distance below the aircraft under typical daytime atmospheric conditions and increases to R = 1.05 at 10 km distance. The calibration uncertainty is in the range of about 1 % to 5 % depending on the background aerosol load. COT can be retrieved in the range from 0.01 to about 2. The depolarization channel is in-flight calibrated following . The calibration uncertainty is estimated to be about 2 % to 5 %. All parameters are provided with a vertical resolution of 15 m and a horizontal resolution of 40 to 200 m depending on the type of along-track averaging. WALES measurements have already been used for studies of natural cirrus and cirrus affected by aviation .

Figure  presents the locations of WALES measurements obtained during the ML-CIRRUS and CIRRUS-HL campaigns. Detailed information on the corresponding segments is summarized in Tables  and , respectively.

The WALES lidar observations of cirrus clouds during ML-CIRRUS have revealed two modes with respect to the median δ of the targeted clouds . Clouds with an air-mass history relating to pristine background conditions were found to show lower values of δ than clouds that could be traced back to originating from more polluted regions. This is reflected in Fig.  by two modes of accumulation of δ at 43 % (low PLDR) and 49 % (high PLDR), respectively. This cloud-history dependent difference in cloud optical properties needs to be considered in a threshold-based approach for identifying embedded contrails as outlined below. Tables  and  thus include a case-based classification according to high and low PLDR conditions .

Meteorological profiles from the European Centre for Medium-range Weather Forecast (ECMWF) ERA5 reanalysis are used in the analysis of the WALES lidar measurements. The hourly data provides a spatial resolution of 0.25° × 0.25° on 37 pressure levels between 1000 and 1 hPa. In this study, we use the zonal (U) and meridional (V) wind components to calculate wind speed and wind direction at intersection points of HALO and commercial flights at typical flight altitudes between 200 and 300 hPa. We consider an averaging period of 2 h in line with the time frame used for aircraft position matching. Wind speed and direction at the intercept of tracks from HALO and commercial aircraft are then combined with speed and heading of both aircraft to account for advection effects as described in the next section. Temperature, pressure, and relative humidity are extracted for further insight into the meteorological conditions at the intercept point.

Data on the position of individual aircraft as available from the airplanes' Automatic Dependent Surveillance-Broadcast (ADS-B) is necessary for an unambiguous identification of embedded contrails . Aircraft position data generally containing information on time, latitude, longitude, flight level, ground speed, and heading of commercial aircraft are necessary for matching them to HALO lidar observations in the framework of the considered experiments. The required data have been procured from Flightradar24 (https://www.flightradar24.com, last access: 19 May 2026). The position information is used here for developing (based on ML-CIRRUS) and verifying (based on CIRRUS-HL) a method for embedded contrail detection in WALES lidar observations. An overview of the aircraft-related parameters necessary for matching their position is provided in Table .

The geometry of the matching problem is displayed in Fig. . Rather than the geometric intercept O that does not account for the time delay between the passage of a commercial aircraft and the HALO observations, we are interested in the point A that represents the location to which the disturbance of a commercial aircraft would be advected by the mean wind. As a consequence, the displacement along the HALO axis of observations OA‾ needs to be determined to identify the true location of a potential embedded contrail. This distance depends on the angles between the different aircraft tracks and the wind direction dir, the wind speed v, and the time delay Δt between the commercial aircraft (tA) and HALO (tH). The last parameter is restricted to 2 h in this study. In contrast to , we do not extend the analysis to situations in which the HALO observations occurred before another aircraft's passage at the same locations. In addition, the search for intercepts is restricted to an altitude range from 8 to 12 km as a range of reasonable overlap of cirrus occurrence and aircraft flight levels . Furthermore, only flights that occurred below the HALO overpass (zA < zH) are considered.

Wind speed and direction at the intersection points O for determining the displacement OA‾ are taken from the ERA5 reanalysis. After determining the angle φ = HA - dir and ψ = HH - dir, the displacement is calculated as 1OA‾=Δtsin⁡ψsin⁡φ⋅vA-1vH-sin⁡ψcos⁡φ+sin⁡φcos⁡ψsin⁡φ⋅v. Any intercepts for which OA‾ resulted in a displacement beyond a HALO overpass' observations are excluded from further analysis.

The predicted position an intercept point depends on the accuracy of the heading of the two aircraft, the time difference between them as well as wind direction and wind speed at flight level. Of those, we consider wind speed to be associated with the largest uncertainty. Given a certain error in wind speed, the location error is exacerbated with increasing time delay. To assess this effect, we have repeated the intercept-point retrieval assuming 1 m s⁻¹ error in wind speed.

The approach for identifying and verifying embedded contrails, based on advected intercepts and lidar observations, is summarized in Fig. . Following the reasoning in that embedded contrails are essentially contrail overlaid to an existing cirrus, we assume that inhomogeneities in cirrus clouds related to embedded contrails should show an increase in ice crystal number concentration and a decrease in ice crystal effective radius as the contrail adds an abundance of small crystals to the existing cloud. In lidar observations, such inhomogeneities should manifest themselves as regions of increased β and COT (more crystals) and decreased δ (smaller crystals appear less non-spherical at the laser wavelength) compared to the surrounding unperturbed parts of the same cloud. However, the challenge is to define suitable threshold values of β and δ that can be used to separate embedded contrails from the unperturbed cloud background. This is realized in the first step of the contrail mask described in Sect. . In addition, the spatial extent of the perturbation should be large enough to be separated from mere signal noise but small enough to still be considered a local inhomogeneity. This will become important in the second step of the contrail mask described in Sect. .

Following the description in Sect. , we first use the information on the position of commercial aircraft and HALO together with the ERA5 winds to identify the location of potential embedded contrails in the HALO observations (gray box in Fig. ). The lidar observations are then used to assess if cirrus was present at the flight level of the commercial aircraft. Intercepts outside the cirrus are discarded from further analysis. For intercepts within the cirrus, the profiles of β and δ at the location of the best match and 10 s prior to that observation are visually inspected for features that agree with the hypothesis outlined above. Specifically, the range from flight level down to 500 m below flight level is assessed for an increase in β that comes along with a decrease in δ, as shown in the example presented in Fig. . Finally, potential contrails from the matching with flight level within cirrus and a β-increase/δ-decrease signature in the lidar observation derived from by-eye inspection are marked as confirmed contrails. Those cases are then used to define threshold values of β and δ for the first step of the automated contrail masking. Subsequently, the automated mask was validated by repeating the procedure with measurements conducted during CIRRUS-HL (see Sect. ).

Here, we will use WALES observations from 12:20 to 13:22 UTC on 1 April 2014 during ML-CIRRUS to illustrate the different steps of the procedure outlined in Fig. . This HALO flight covered the northern part of Germany (see Fig. ). It focused specifically on observations of contrails and contrail cirrus and, therefore, features a very high likelihood of containing cases of embedded contrails. The observation of WALES on 1 April 2014 corresponds to cirrus clouds under polluted high-PLDR conditions (see Table ). This circumstance becomes relevant later in the analysis when the confirmed embedded contrails are used to obtain a threshold-based detection mask.

First, the information on the position of commercial aircraft passing through that region is matched to the HALO track with intercepts advected with ERA5 winds as described in Sect. . This gives the locations of embedded contrails along the HALO track as shown in Fig. . By considering the actual lidar observations, only cases with a confirmed cirrus cloud at flight level are retained for further investigation.

Figure  reveals the presence of several cirrus layers during the noontime observations of 1 April, including an approximately 1 km deep, relatively homogeneous layer during the first half hour, beneath which more heterogeneous cirrus with strong virga extending down to 6 km can be seen. The increased COT from 12:50 to 13:05 UTC is related to the cirrus shield of a deep-convective cloud that attenuates the laser light at altitudes below 8 km. The final 15 min of the measurement show another cirrus layer with a cloud top at 11 km height but now featuring extensive virga down to 8 km. In general, increased COT results from a stronger backscatter signal, which is considered a signature of a potential embedded contrail. In addition, candidates for embedded contrails are often found in regions of lower δ. While both observations are in line with our hypothesis outlined earlier, we are interested in quantifying these differences to establish objective thresholds for identifying embedded contrails solely based on the lidar observation.

Figure  illustrates the subsequent investigation of two candidates for embedded contrails marked in Fig. . The profiles of β and δ at the location of likely contrail occurrence are compared to those observed 10 s later. If there are no marked differences in the profiles related to the cloud regions that we assume to be perturbed and unperturbed, respectively, the case is not considered an embedded contrail (Fig. a). This corresponds to the heterogeneity requirement that forms the second step of the contrail mask presented in Sect. . In lidar measurement, the increase in β indicates a higher number of scatterers, corresponding to an increased concentration of ice particles , while the decrease in δ, which is sensitive to particle size and shape , suggests the presence of smaller and less non-spherical (with respect to the laser wavelength) ice crystals. These features are characteristic of regions perturbed by aircraft passage, typically found about 500 m below flight level . Therefore, cases that show a marked increase in β and a decrease in δ within the identified region of likely contrail occurrence (Fig. b) are considered as confirmed contrails. An overview of the number of cases for the example of 1 April 2014 is provided in Table .

This by-eye inspection presented in Sect.  was performed for all intercepts identified in the WALES observations during ML-CIRRUS (see Table ) for selecting thresholds of β and δ for the automated identification of embedded contrails described in this section. The analysis was then repeated using WALES observations from CIRRUS-HL (see Table ) to obtain a dataset for assessing the quality of automated embedded contrail identification with ML-CIRRUS-based thresholds. An overview of the number of cases for ML-CIRRUS and CIRRUS-HL is provided in Table .

The analysis of the ML-CIRRUS dataset led to the identification of a β threshold of 4 Mm⁻¹ sr⁻¹ for the detection of perturbed cloud regions. This relates to an increase in the detected backscatter signal that results from the increase in ice-crystal concentration that occurs when a contrail is added to the already existing cloud . In contrast, the occurrence of high and low PLDR cases in the ML-CIRRUS dataset inhibits the use of a fixed δ threshold for contrail identification. To address this issue, the 2d histogram in Fig.  is separated according to high and low PLDR conditions as shown in Fig. . Together with plotting values of the individual cases (such as in Fig. ) within the same space (contrail cases occur predominantly in the upper-left parts of the plots in Fig. , not shown), these 2d histograms (as representative for the entire ML-CIRRUS data set) have led to the choice of 30 % and 43 % as δ threshold for low and high PLDR conditions, respectively. The lower values of δ in the perturbed region of the β-δ-space represent the fact that the ice crystals formed after an aircraft's passage are much smaller than those of the already existing cirrus, which leads to a crystal ensemble that appears less non-spherical in the context of a depolarization lidar measurement compared to the unperturbed cloud. The thus obtained threshold values separate what we consider here as unperturbed and perturbed regions of a cirrus and are used in the first step of the contrail masking. The robustness of the selected threshold values has been evaluated in a sensitivity analysis in which β is lowered to 3 Mm⁻¹ sr⁻¹ and δ is increased to 35 % and 45 % for low and high PLDR conditions, respectively. The comparison of contrail occurrence for different variations of threshold values is presented in Table .

Observations with combinations of β and δ that fall in the perturbed sectors in Fig.  are not always related to embedded contrails. For instance, regions of strong backscatter signals that approach detector saturation (such as between 12:54 and 13:05 UTC in Fig. ) often coincide with weak perpendicular backscatter signals that lead to PLDR values below the δ-threshold. Such larger-scale signatures can be associated with the upper part of deep-convective systems or fall streaks – as also apparent from the combination of Figs.  and . To address this problem, we apply an inhomogeneity condition that is in line with how embedded contrails are defined in the manual analysis. Specifically, we assess the size of the unique objects identified in the contrail mask after step one, i.e., eight-connected areas identified as perturbed cloud. As a conservative estimate, contrails up to an age of 2 h show a typical cross section of 500 m height and 1000 m width . Considering the lidar grid of 15 m vertical and 200 m horizontal resolution, this would refer to a maximum object size of 165 pixels. However, the cross-section of a real contrail is not rectangular and, thus, unlikely to fill this entire box. In addition, such a size would only apply if the observation during the intercept was perfectly perpendicular to the contrail. For a more realistic selection of the threshold values for the inhomogeneity assessment, we go back to the verified contrail cases from the manual analysis. From this, we conclude that objects should contain between 10 and 50 pixels to be considered an embedded contrail. Smaller features are considered as noisy data, while larger features are not in line with our underlying assumption that embedded contrails are a locally constrained cloud perturbation. The result of allowing for smaller or larger feature size on contrail detection is shown in Table . The selected pixel range is rather inclusive as shown in the examples in Figs.  and . However, a more conservative contrail mask is more likely to be transferable to WALES observations during other HALO campaigns compared to one that is tuned too much towards the ML-CIRRUS and CIRRUS-HL observations. While the thresholds of the physical parameters applied in step one are directly transferable to observations with other airborne lidars, we would like to point out that the size of acceptable contrail objects in step two might need to be adapted to the spatio-temporal resolution of the respective instrument.

Figure  illustrates the application of the two-step contrail mask to the WALES observations on 1 April 2014 in Fig. . No contrail masking is provided below 8 km height as there is generally little (contrail-producing) air traffic below that height. However, observations down to 7 km are still considered during step two to properly consider larger perturbed cloud regions of which only a fraction smaller than the upper size limit extends above the lower cut-off height, such as in the cloud present below 9 km height until 12:36 UTC. For the case of 1 April 2014, the majority of the cloud area is identified as unperturbed cloud. This is in line with the by-eye inspection of the confirmed matches – most of which are true negatives. Table  shows that 175 out of 189 matches within clouds relate to lidar observations without a distinct contrail structure identified by the human observer interpreting data as in Fig. . Figure  shows a number of large areas (between 12:54 and 13:05 UTC or between 13:10 and 13:19 UTC) that pass the β-δ threshold but are clearly too large to represent actual contrail structure. These homogeneous areas are re-labeled as cirrus after the second step of the masking. This intermediate outcome (orange areas in Fig. ) is not displayed in later presentations of the results of the contrail masking. The final contrail mask reveals a number of small areas (e.g., at around 12:30, 12:34, 12:48, or 12:58 UTC) that appear to be reasonable representations of embedded contrails. For the areas around 12:34 and 13:20 UTC, the contrail-labeled points located within the blue region mark true positives. Other blue dots, while not representing straight hits, are mostly in the vicinity of blue areas – so that the small spatial differences might be attributed to the uncertainty in the advection correction using modelled mean winds. Finally, false negatives, such as around 13:02 UTC, can occur when the contrail perturbation is located in a larger area that passes step one but not step two of the analysis. Such cases might require an adaptation of the β-δ thresholds that could be realized, e.g., by introducing an iterative loop to step one of the contrail masking. Finally, the error bars on the location of the intercept points indicate scaling with the time delay between the two aircraft, i.e., the temporal difference dominates over the wind-speed error. Lowering the accepted time delay of currently 2 h would be a straightforward measure for reducing the error in the location of the projected intercept points.

By design, the methodology presented here was intended to be applicable to lidar measurements of β and δ without the need for internal input. Further constraints are introduced by accepting only identified perturbations of a certain size. The latter requirement is particularly efficient for screening out signal noise and large-scale features that relate to the upper part of deep-convective systems of fall streaks, such as in Fig.  after 10:54 UTC. However, fall streaks do not necessarily extend beyond our 50-pixel threshold as visible on 12 July 2021 in Fig. . While such cases represent misclassification in the context of the intended contrail masking (as we are not able to connect them to an aircraft in our flight-track dataset), they are indistinguishable from embedded contrails as defined according to our mask, i.e., in the optical properties. As such, they are worth keeping for further study. More insight on the performance of the contrail masking will be obtained from the now possible statistical investigation of contrail microphysical properties from synergistic lidar-radar observations in which the combination of contrails (higher number concentrations, smaller ice crystals) and fall streaks (lower number concentration, larger particles) should manifest as bi-modal distributions of ice-crystal effective radius and number concentration, whose modes might be used for further data screening.

Table  underlines the necessity for the comprehensive data screening described above. For ML-CIRRUS, a total of 3115 intercept points are found between HALO and commercial aircraft within a time difference smaller than 2 h. 724 cases out of those are rejected because advection caused them not to be covered by the WALES lidar observations. Out of the remaining 2391 cases, 1800 are found to relate to aircraft passages outside cirrus. The total number of 536 in-cirrus cases is dominated by situations in which lidar observations do not indicate a marked difference in β and δ in the likely affected height region. Finally, the entire ML-CIRRUS data set features 55 confirmed embedded contrails. In the CIRRUS-HL campaign, 58 out of 699 in-cloud cases are classified as embedded contrails.

Figures  and provide statistical information on the distribution of the time difference between commercial aircraft and HALO, the flight level of the commercial aircraft, the wind speed at flight level, and the related displacement of the theoretical intercept point for the different levels of screening in Table . In summary, little difference in found in the conditions for embedded contrails compared to all cases. Displacements are generally smaller than 50 km. Conditions during ML-CIRRUS and CIRRUS-HL are different only in the form of higher wind speed at flight level during the latter campaign.

Table  summarizes the statistics of identifying perturbations with the contrail mask for ML-CIRRUS and CIRRUS-HL. More details of the impact of the choice of threshold values and feature size are provided in Table . Based on the fraction of perturbed pixels, contrails account for only around 1 % of the lidar data within cirrus clouds, with a more stable fraction during low-PLDR conditions. However, the low fraction of perturbed pixels under high-PLDR conditions during CIRRUS-HL is probably related to the predominance of more pristine cirrus conditions sampled by that campaign. A better quantification is thus provided by considering the number of objects that remain after applying the contrail mask, which can be directly compared to the number of embedded contrails identified in the manual analysis. We consistently find more perturbed objects than manually identified embedded contrails, which was to be expected. On the one hand, the automated analysis cannot separate between embedded contrails and other small-scale perturbations that pass the β-δ screening as outlined in the previous section. On the other hand, the manual analysis can only account for aircraft that are included in the waypoint data set used for location matching.

Nevertheless, we find a stable overestimation of a factor of four for observations during low-PLDR conditions for both campaigns. This gives us an idea of the false detection rate. The performance of the contrail masking is worse during high-PLDR conditions. This is not unexpected as a larger range of observations in terms of δ can pass the first step of the filtering. In the future, further layers of the contrail masking could focus on a better screening of fall-streak signatures to reduce the number of false positives.

Figures  and show a large number of red circles that refer to intercepts for which no contrail signature was identified in the manual analysis. In general, those cases are also classified as background in our masking and we consider them to represent true negatives. show that potential contrail-cirrus regions (PCCRs) almost always coincide with regions that are already covered with subvisible or visible cirrus. They define PCCRs as air masses with a relative humidity over ice larger or equal to 90 % for which the Schmidt-Appleman Criterion SAC, is fulfilled. However, this does not imply that all cirrus regions are also PCCRs and that an aircraft that passes through a cirrus cloud automatically forms an embedded contrail. For instance, a dissolving cirrus at ice-subsaturation might support contrail persistence but will not promote contrail formation.

For our cases of contrail absence, true negatives might refer to conditions for which SAC is not met. Alternatively, we can also expect that the detectability of the contrail imprint on the considered optical properties is time dependent. Very young contrails feature very small ice crystals that are not yet detectable in optical measurements while dispersion weakens potential contrail signatures over time until they become indistinguishable from the cirrus background . We have investigated the potential time dependence of contrail detection by contrasting the distributions of the time delay between an aircraft's passage through cirrus and the subsequent WALES lidar observations for manually confirmed and rejected contrail cases. Figure  highlights that contrail cases show a larger occurrence rate for time delays (contrail age) between 10 and 40 min while rejected cases are almost equally distributed over the considered 2 h time period. The reduced occurrence of contrails for very short delays of a few minutes and for delays that extend beyond one hour indicates that there might be a temporal sweet spot for detecting embedded contrails in lidar observations that depends on the microphysical processes related to different stages of the contrail life cycle . In line with the low detection rate for contrails in the vortex phase, have dismissed the first 5 min of time delay between an aircraft and a spaceborne lidar observation in their analysis of the global net radiative effect of embedded contrails.